EXN.2.SL.TZ0.4

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The following table shows the systolic blood pressures, $p$ mmHg, and the ages, $t$ years, of $6$ male patients at a medical clinic.

The relationship between $t$ and $p$ can be modelled by the regression line of $p$ on $t$ with equation $p = a t + b$ .

A $50$ ‐year‐old male patient enters the medical clinic for his appointment.

Determine the value of Pearson’s product‐moment correlation coefficient, $r$ , for these data.

[2]

a.i.

Interpret, in context, the value of $r$ found in part (a) (i).

[1]

a.ii.

Find the equation of the regression line of $p$ on $t$ .

[2]

Use the regression equation from part (b) to predict this patient’s systolic blood pressure.

[2]

A $16$ ‐year‐old male patient enters the medical clinic for his appointment.

Explain why the regression equation from part (b) should not be used to predict this patient’s systolic blood pressure.

[1]

Markscheme / solution

* This sample question was produced by experienced DP mathematics senior examiners to aid teachers in preparing for external assessment in the new MAA course. There may be minor differences in formatting compared to formal exam papers.

$r = 0.946$ A2

[2 marks]

a.i.

the value of $r$ shows a (very) strong positive correlation between age and (systolic) blood pressure A1

[1 mark]

a.ii.

$p = 1.05 t + 69.3$ A1A1

Note: Only award marks for an equation. Award A1 for $a = 1.05$ and A1 for $b = 69.3$ . Award A1A0 for $y = 1.05 x + 69.3$ .

[2 marks]

$122$ (mmHg) (M1)A1

[2 marks]

the regression equation should not be used because it involves extrapolation A1

[1 mark]

Examiners’ report

[N/A]

a.i.

[N/A]

a.ii.

[N/A]